Ricci semisymmetric almost Kenmotsu manifolds with nullity distributions

Abstract

The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to the (k, µ) -nullity distribution and (k, µ)-nullity distribution respectively. Finally, an illustrative example is given.

Pseudo-symmetric structures on almost Kenmotsu manifolds with nullity distributions

“…Thus we arrive to the following corollary. This generalizes the result of Deshmukh et al [5]. The above corollary can be verified by the example given in [4].…”

“…Pseudosymmetric almost Kenmotsu manifolds have been studied by Wang et al [13]. In the present paper, we study some curvature conditions imposed on the Ricci curvature tensor of almost Kenmotsu manifolds with (k, µ)-, (k, µ) -and generalized (k, µ)-nullity distributions, by generalizing the results of Deshmukh et al [5], and Wang et al [13].…”

“…Among them, Wang and Liu [11] study ξ-Riemannian semisymmetric almost Kenmotsu manifolds satisfying (k, µ) -nullity and (k, µ)-nullity distributions. Recently, Deshmukh et al [5] studied Ricci semisymmetric almost Kenmotsu manifolds with nullity distributions. Pseudosymmetric almost Kenmotsu manifolds have been studied by Wang et al [13].…”